We present a method for reconstructing the radial density profile of a cylindrically symmetric object from a single x-ray projection, when the profile consists of a number of different constant sections. A forward Abel transform based algorithm is employed whereby the profile is recovered recursively, onion peelinglike, starting from the outside diameter of the object and moving in. Distortions originating in the Gibbs phenomenon, unavoidable in most available Abel inversion methods, are completely eliminated. The method is simple enough to be carried out on a handheld calculator or a spreadsheet program on a personal computer, and no elaborate computer fits or application programming are required. The method is demonstrated by inverting a simulated three-section noisy set of data and is shown to yield results of a quality equal to that of a recent powerful Abel inversion method, based on full nonlinear least-squares computer fits.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.